# Numbers such that Tau divides Phi divides Sigma/Examples/3

## Examples of Numbers such that Tau divides Phi divides Sigma

The number $3$ has the property that:

$\map \tau 3 \divides \map \phi 3 \divides \map \sigma 3$

where:

$\backslash$ denotes divisibility
$\tau$ denotes the $\tau$ (tau) function
$\phi$ denotes the Euler $\phi$ (phi) function
$\sigma$ denotes the $\sigma$ (sigma) function.

## Proof

 $\ds \map \tau 3$ $=$ $\, \ds 2 \,$ $\ds$ $\tau$ of $3$ $\ds \map \phi 3$ $=$ $\, \ds 2 \,$ $\ds$ $\phi$ of $3$ $\ds \map \sigma 3$ $=$ $\, \ds 4 \,$ $\, \ds = \,$ $\ds 2 \times 2$ $\sigma$ of $3$

$\blacksquare$